{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from numpy import random\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Maslov_model(N, buy_sell_param, qlo, bid_limit_orders, ask_limit_orders, initialPrice):\n",
    "    prices=[initialPrice]\n",
    "    for i in range(N):\n",
    "        u = random.uniform()\n",
    "        if u<=buy_sell_param: #Buyer - BID\n",
    "            v = random.uniform()\n",
    "            if v>qlo and ask_limit_orders:#Market_bid\n",
    "                price = ask_limit_orders.pop(0)\n",
    "                prices.append(price)\n",
    "            else: #Limit_bid\n",
    "                delta = random.uniform(0,4)\n",
    "                order = max(prices[-1]-delta,0)\n",
    "                bid_limit_orders.append(order)\n",
    "                bid_limit_orders.sort()\n",
    "                prices.append(prices[-1])\n",
    "        else: #Seller - ASK\n",
    "            v = random.uniform()\n",
    "            if v>qlo and bid_limit_orders:#Market_ask\n",
    "                price = bid_limit_orders.pop()\n",
    "                prices.append(price)\n",
    "            else: #Limit_ask\n",
    "                delta = random.uniform(0,4)\n",
    "                order = prices[-1]+delta\n",
    "                ask_limit_orders.append(order)\n",
    "                ask_limit_orders.sort()\n",
    "                prices.append(prices[-1])\n",
    "        #print(\"ask_limit_orders sep %i\" %i, ask_limit_orders)\n",
    "        #print(\"bid_limit_orders sep %i\" %i, bid_limit_orders)\n",
    "    return prices\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import OrderedDict\n",
    "\n",
    "## Expiration time for each limit order is added\n",
    "## list of orders are dictionaries\n",
    "\n",
    "\n",
    "def Maslov_expiration_model(N, buy_sell_param, qlo, bid_limit_orders, ask_limit_orders, initialPrice, expiration_time):\n",
    "    prices=[initialPrice]\n",
    "    times = [expiration_time] * 10\n",
    "    bid_expiration_times = {i: times[i] for i in range(10)}\n",
    "    ask_expiration_times = {i: times[i] for i in range(10)}\n",
    "    number_bid = 10\n",
    "    number_ask = 10\n",
    "    for i in range(N):\n",
    "        bid_times_to_delete = []\n",
    "        ask_times_to_delete = []\n",
    "        for key, time in bid_expiration_times.items():\n",
    "            if time < i:\n",
    "                try:\n",
    "                    del bid_limit_orders[key]\n",
    "                except KeyError:\n",
    "                    print(\"pb\")\n",
    "                bid_times_to_delete.append(key)\n",
    "        for key, time in ask_expiration_times.items():\n",
    "            if time < i:\n",
    "                try:\n",
    "                    del ask_limit_orders[key]\n",
    "                except KeyError:\n",
    "                    print(\"pb\")  \n",
    "                ask_times_to_delete.append(key)\n",
    "        for key in bid_times_to_delete:\n",
    "            del bid_expiration_times[key]\n",
    "        for key in ask_times_to_delete:\n",
    "            del ask_expiration_times[key]\n",
    "        u = random.uniform()\n",
    "        if u<=buy_sell_param: #Buyer - BID\n",
    "            v = random.uniform()\n",
    "            if v>qlo and ask_limit_orders:#Market_bid\n",
    "                index = next(iter(ask_limit_orders))\n",
    "                price = ask_limit_orders[index]\n",
    "                del ask_limit_orders[index]\n",
    "                del ask_expiration_times[index]\n",
    "                prices.append(price)\n",
    "            else: #Limit_bid\n",
    "                delta = random.uniform(0,4)\n",
    "                order = max(prices[-1]-delta,0)\n",
    "                bid_limit_orders[number_bid] = order\n",
    "                bid_expiration_times[number_bid] = (expiration_time + i)\n",
    "                bid_limit_orders = sort_dict(bid_limit_orders)\n",
    "                prices.append(prices[-1])\n",
    "                number_bid += 1\n",
    "        else: #Seller - ASK\n",
    "            v = random.uniform()\n",
    "            if v>qlo and bid_limit_orders:#Market_ask\n",
    "                index = list(bid_limit_orders.items())[-1][0]\n",
    "                price = bid_limit_orders[index]\n",
    "                del bid_limit_orders[index]\n",
    "                del bid_expiration_times[index]\n",
    "                prices.append(price)\n",
    "            else: #Limit_ask\n",
    "                delta = random.uniform(0,4)\n",
    "                order = prices[-1]+delta\n",
    "                ask_limit_orders[number_ask] = order\n",
    "                ask_expiration_times[number_ask] = (expiration_time + i)\n",
    "                ask_limit_orders = sort_dict(ask_limit_orders)\n",
    "                prices.append(prices[-1])\n",
    "                number_ask += 1\n",
    "        #print(\"ask_limit_orders sep %i\" %i, ask_limit_orders)\n",
    "        #print(\"bid_limit_orders sep %i\" %i, bid_limit_orders)\n",
    "    return prices\n",
    "\n",
    "def sort_dict(dict):\n",
    "    ordered_dict = OrderedDict(sorted(dict.items(), key=lambda x: x[1]))\n",
    "    return ordered_dict\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112213f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 100000\n",
    "buy_sell_param = 0.5\n",
    "qlo = 0.5\n",
    "bids = np.linspace(990,999,10).tolist()\n",
    "asks = np.linspace(1001,1010,10).tolist()\n",
    "ask_limit_orders = {i: asks[i] for i in range(10)}\n",
    "bid_limit_orders = {i: bids[i] for i in range(10)}\n",
    "initialPrice = 1000\n",
    "expiration_time = 1000\n",
    "prices = Maslov_expiration_model(N,buy_sell_param,qlo,bid_limit_orders, ask_limit_orders, initialPrice, expiration_time)\n",
    "\n",
    "fig = plt.gcf()\n",
    "fig.set_size_inches(18.5, 10.5) \n",
    "plt.plot(range(N+1),prices)\n",
    "plt.title(\"Modèle de Maslov pour N=%i et qlo=%.1f et expiration_time=%.1f\" %(N,qlo,expiration_time))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-5, 5)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1122137b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "##Dsitribution of p(t + time_lag) - p(t) \n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "time_lag = 1\n",
    "x = []\n",
    "for t in range(N):\n",
    "    if t + time_lag < N:\n",
    "        x.append(prices[t + time_lag] - prices[t])\n",
    "\n",
    "fig = plt.gcf()\n",
    "fig.set_size_inches(18.5, 10.5) \n",
    "plt.hist(x, bins = 1000)\n",
    "plt.xlim(-5, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112ab8a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def log(x):\n",
    "    y = []\n",
    "    for i in range(len(x) - 1):\n",
    "        if x[i] > 0 and x[i + 1] > 0:\n",
    "            y.append(math.log(x[i + 1]) - x[i])\n",
    "    return y\n",
    "\n",
    "y = log(x)\n",
    "t = [math.log(n) for n in range(1, len(y) + 1)]\n",
    "plt.plot(t, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Further on introduce a Maslov model with expiration time for limit orders"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "OrderedDict([(1, 23), (3, 34), (2, 45)])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dict = {1 : 23, 2 : 45, 3 : 34}\n",
    "sort_dict(dict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109a28f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 100000\n",
    "buy_sell_param = 0.5\n",
    "qlo = 0.5\n",
    "bid_limit_orders = np.linspace(90,99,10).tolist()\n",
    "ask_limit_orders = np.linspace(101,110,10).tolist()\n",
    "initialPrice = 100\n",
    "\n",
    "\n",
    "prices = Maslov_model(N,buy_sell_param,qlo,bid_limit_orders, ask_limit_orders, initialPrice)\n",
    "\n",
    "fig = plt.gcf()\n",
    "fig.set_size_inches(18.5, 10.5) \n",
    "plt.plot(range(N+1),prices)\n",
    "plt.title(\"Modèle de Maslov pour N=%i et qlo=%.1f\" %(N,qlo))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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In7rphbiLgAQjsBGQhtYezd7SEncxgKpxQsRRi6N9w7p/1b5oVwog0d5+8fP6yLXpGFZmefIFUq2htUfn3Fev4dHxuIsCpNKJcRegWnzoaqfi03TZGTGXBKgOxkd/jCDq8z94ZKOW7m6rfEFADcqcrdX2cN3eO6z23uG4i4GUqmSYJD0Sa89Pn9yitU2d2tjcpXf+xatiKcPBLqZ7RXrRYwNAInkZ25nJwxHEs9TRPrqwA0iv6gopgf2JOPQOjsZdBKBsBDYAAEAg4noY4yGQHAwAgNpGYAMAAAQi7odruu9XLz8zZcVpR8uxuIsAADWJwAaARPLygJTUau7NixviLkJZ4n4oRfox9fJkgyNj+vHjm9TRG/5Qt2rc9iNjx5MoJvV6n4vEj6hUteUqAqJCYANA6iWtCnDH0sa4i+BLWh4YkHzUxyebtfGgHq0/oMvn7Cz6Oc7B/C6bXXy7VZtqDE4hXbKPQK7nSBsCGwBSKyU9kwHUgBkrmzR/+5G4i1FV1u/vnPh3Wq732eXkwRDlSMuwKyBpCGyErLNvWNOm1+nu5S/GXRQgVbivO2ZuOKhp0+vUMzgSd1GAkmJLHpqAJ8jzZ23TN++rj7sYAFC2g10DE/+mHoa0IbARspbuQUnSo/XNMZcE1eDY4Ig+ceNy7W3rjbsoiRLEQ40JsDN4Z39wQYgfPLJRkrT5QHdgywSCktt1Pu74Ai2d1Sstuzb7XpKWMgMZT64/GHcRUm/7IRIIx4XABpAiC3e0avOBbl2/YE/cRUkIao1AEhwPKMTfcwLVKcjgM6pDEnpqhaFaf1ctuPDpbfrY9ct0waytcRelJhHYiEh2Zm+gXLWUWGxwZCzuIgCxs9bqhgV71B7BrBqVoCKeAOyCRKCXRnQeX3cg7iIAk9yzokmSdO/KffEWpEadGHcBql33gNMlfW9bX8wlQTXIPDvUQr2pqaPf82epz1e/5qPej4dqUr+vU1c9v1sbmrviLkpeSWtFJ8CCJKnkcEzWmZVMu4/0xF2EUDCkDigPgY2Q9Q+Pxl0EVCFueg42Q7CS3CNo1sbaHPeb6e2XnnsJJ2Vcknv2lm9jQgN6adUzOKLhUXoQA6hODEUBUoTGyPxqYbs06TtiAAAgAElEQVSE+RsJlKFa1PKxnJTrYFf/sM6+faVaugdKf7iESb+pdndtYN596UKddvH8uIsRmKQc8wCSgcAGyvKdGeviLkJNo37niGM7pKflHEDconrw6khQDpYn1x/Uqsajum1JY9xFSbUwDp2eIe5fGUnO48WQOqA8BDZQljnbDsddBCAQmTw4Xht6f/ns9hBLA6TH3rZerWk6GncxUiHMXCTPbDqk0y6er3X7OkNbB7yr4U5Dkavk8f/YQHDTsgclaTmLgLQhsAEkSEv3QNEeAcTwCylvyzxW36xTL5qnHS3e5xxftLOtrHUBZXEP7cGR5I2LX7DjSNxFgKRVjR2SpO0t3TGXJFxpfOQL8p6d5BxIcam2jg1J28dpPOdQ2whshIzIPfz4x0sX6nO3rSz4vq2laVE8qPT8WrLbCVLsae31/J3DxwYrWyngw7ztTvAgiUkUsx8q4s5tkfYHHOoKADLivp4CaVVxYMMY82fGmEXGmB3GmG3GmP9xX3+VMeZ5Y8we9///sPLiIkq7DvfouS0tcRej5mw9WLr3AN0VJwvioSbpD0ZJa8mJWtL3T1j6GBOfagc6nQSa4yEewLVyavCwh1y1fl8EMFkQPTZGJf3QWvs3kt4l6XvGmDdJmi5pgbX29ZIWuH/XnDRXxj987VJ994H1cRejqMPdg+ruT944ybCk+HAKRRIDPFsPVnd38Lj0JzjRWzV4rL6ZoSUhuHFRgyRp2yHvw92Qbhv2J693FdKF5KH+PVrfrMPd9KitdRUHNqy1Ldba9e6/eyTtkPQaSZ+UdK/7sXslfarSdQG53nXpAp1++cK4ixG5am64Ghkb1+hYNPkEDnY5ralBtoqfecPywJaF425ZvDfuIiSS18z+rT2Den574cDFjx7frG/cWx9UsQrq7h+pqWB0FDK3g7ifheZvPxJqcCwtt73Fu1rjLkLNaO0pfzagJIYOktZYk8RtlE/3wIh+/Phmffmu1XEXZUI119OTLNAcG8aYaZLeJmm1pD+x1rZITvBD0h8X+M45xph6Y0x9WxtJ+ZLsQ1cv0eeL5H+IC9OXVZc3nDdb771ika/vlHvzzbSszUvBLD9j4xFUMdJSi4Ek6djgiN54/hxPnz379lX61n31GgkwaFjO4XLqL+bp1F/MC6wMSI5v3levb9xbz2Uk6+G0UMv7ncsadeHT26IqUNWq25z84dLL97Srsc1bHi+G1pQnc561VRDoQnUILLBhjHm5pCck/cBa67nPpbX2dmvt2621bz/ppJOCKk5iVFPErqG1V6tfZGq/WNXAPc9a6ZDH7oSZ8yuIlsqkn6thtsYm/KfXtGK7vbNv2PNy9nf0V16YIjIVy6SfR3547Q0Tt6TeFoI+Fqrp2Lq4bofuWdEU6ToPuT0U4Vgf0fTIX75rtT5w1RJf3yGfjD8vtvdJcnpuJAV7MB6BBDaMMS+VE9R4wFr7pPvyEWPMn7rv/6kk+uYhUM1Hw62oJ1Emms8FEwDCtS6iB5+g8CyUDEHth6B3Z0s3gY1sFz6T7B4zTe19+o/frNHAcDoCrHF6bN2BuIuAhAhiVhQj6S5JO6y1V2e99bSkr7n//pqkWZWuC8i2p7Un7iLEhgpssGgdAYIRd1fgIE/l0QCHf0VxiYk7xwaSLYrRjGmStHwW2ay1+uWz27VoV5teaGiPuzhAapwYwDLeI+krkrYYYza6r/1M0mWSHjXGfEPSfkmfDWBdAEQFNoN4RDA4nOBXZ9+wZm08FHcxQhXkzASRBDbCX0WskvwgCgSBY7w8SdxqNJjFo+LAhrV2uQofUx+sdPlAIbX4cM9NLxxsVRcbInGSep378l2rtaPleDqtpFTikrC9xsatvnHvWv3n+/5q4rUoynWgs7qHGiTkECspJcWseSTqLM2oegOmo2PjetelC/TTj/6NPnPaKXEXBwEJoscGikjrg2hDq7cMzkCckvAQA9SibYc85wivOR29Q1q8qy3ybeQnmWwapbE2VcktittbuJJYf8gXbElgMavC0b5htfcO64ePbQolsBFkjz94F+h0r8gjjXdiSY+s3R93EUpKS+tNkGhhyC+sY2Ha9LrETHHMvgeilZReKGlTboV+5d6OotNap+UKyGGDShljOI6AMhDYQGrVcjCUG17wCm3SsKY43nW4R9Om1yVr5oUAzqnzZm7RGdcvq3xBNWJVY4fWMI12YLg2JoefHqvL9rTpC3es0q1L9oZYIiAdrLU1XcetBidwM4oFgQ1E6qE1+/W3F87VOOm5kSBx3H+W7m6TJM3e0hL9ynME+fPvX7WfYQo+nH37Kn2uzF5BaR3qWIuo4xbX0j0oSXqxvW/itfomAn4IT1tvvDM45cM1PTphP4VwzY8HOTZQ0l3LX9SKgKab+umTWyQ50+i97ATO+nIRyXd43Q49gyM63D2o1//J74dbIIRiLQ84sRkeHdfAyJhe+TsvjbsoqRbmNbta7we5veWoMVSG7TdZ0s8bHoy9Y1shgx4byCv7gv/LZ7drwc7Wipe5aFfly6h15UbzrbUaHRsPuDTp8dW71+hfrlka+np6h0ZDX0ct+uytychzUou+c/86nXrRvLiLEYuv3b3G82eTcH1Ncx6e1Y0egpcpeXgZGj1+LCT94RnJkuZzOE70dEEGgQ1E5lBXdU9FF4ViN71jgyM6+/b8D4Dnz9qq1507O6xixcZrlH7D/q5wC+IKM18GFWTEYWEAQe0oxH1+jMVdAMW/DSrxxPoDcRchMIt3tcVdBKRcduJiZtcAvCOwEbaYr0fWWjW2Vd/UrQc6+zUwMhZ3MSLV1N6ni5/dISn/A/3sLS1aVaDV6/5VyZ/lppY9vGa/DpYI/FG3QRqt39+pM65fpsGIrteFgp3WWvUPR9ujKqpztpq6YXOdO27Kbq1g29RtbtH+o/2VFAcRcoIZ8Z/YaTkd6emCDAIbVWLdvk5Nm16nw24CroyH1zbrA1ct0erGjphKdlyQFZbTL1+k/3pwQ3ALTIHv3L9OPQx1mCS4Yyq+CkTf8KimP7lFX7xjVWxlAMJy0TPbte3QMe1oiTeh7PULGvSmn89VV/9w+CuL+HJSK8EAupuX73sPrtf/Prop7mKghMnHeI2c2FViR8sxTZteN/E316t4ENioEvev2idJWrF3cpLPTc1OF/zGrEzjXnA5TZ4xZpIpKI23j8Z2pydVZr8e7Y3ggQupU6wlilYq72ZtPChJ6ugL5zw7/fJFRd+vpl4VXgX9m2txGwJxSsspl4Tg7nMJmOEOBDZCNxrxw2gSTm6Ej/0crDgqzA+taZYktfUkZ8o5DqtkGBu3unLuTqd3QZXslCr5GQVNOo9j+rFBVzdWNXaoI8YpMZMYyHixvU/TptdNNBp5tfVgt6ZNr9PKvfH3nq1m21M+1fjkYHUCT4AUONAZ7JCrzQe6NG16XWrzBI6PW107f7c6QwrqJw2BjZCdN3NLJOvJtEYVkoQHYTvp3wkoUMqU2mJ0e4tfWpN8JfEBIkl2H+nRzYsbIlvf/B1HdNOivbrome2RrTMstXxoRX9eBXv9Ofv2Vfr87fENkcu9nCbhWFrkJtN9akPxOleuTG/ahTuPBF4mHPex65fFXQRU6Mt3rtbVz+8u+/sjY96ug16ra7ctbZQkLduTzqTAS/e06dr5e3TerK1xFyUSBDZCduRYNK0dSR+lcGxwROfPrI2TKgrlVpjT+uBdSNQBsjC2X3Xtker0qZte0BVzdkU2peeoWzEbGi2ecDMNwcykHN9JKUfaNLRGm3ycRg9Uk3GflfN81/RaOyOWN7Tr+gV74i7GhLrNzhCTjc3dMZekPMPu9NPHBkZiLkk0CGxUmUIXQL8PwkE/v83aeCiwZTWT2RsJVdFpk/xn1Jo15FYMaq2CWY04zRCHoRFvQdFiwcov3rla//Xg+qCKhAgMVxAMpydlsvidVSsp++8ZNzCzbE97iU9WBwIbNaKaGupLDbsJQlf/sFqPDZb+YISC6C1QTceBlI4W61ImfkGV7ZtqktlHQZ8/V87dWfIzQR8WUV8Dss/QTMtRmEr9Pk6z/Lr6hyPvneGXScqTQhmu8ti1PrvHSr5j9dnNJCisVvs7+rWm6ejE39VWXwtTEjdVUi5XkcwEliAENqpMJQ+/D6zep6W70zmGLGinXTxf7/zVgriLUVDe3ezhIprEi3+ahFHRSHNlvVac4O6joLvJ37Rob9H3+4eLD0XxIwmH2UyfeQmCFMfPz75ehBWEHRod00Nr9k9Zn19nXL9cH7p6SSBlCuo6mXvMJmEo5V3LX4y7CFWn9dhgzSQ2LObx9Qfyvn7t/OQMy/Bjf0d/ZAk3J19rUcsIbNQIL5Xac5/aqq/evSb8wlQoiroNU6vWljhvhEmorKME9wCJaldlrteLd1VXoHlkPPweG4XudZGeZWVcUMo9tu5wE9tV6mAIDyDlXFeT3Auvo3fI/3bi8l7SO3+1QG/75fNxFyN+OReBzLVsR0s6Z3p575WL9O7LFsZdjNQ5cmxQD67eH3cxUovARo3g2Wmy0bFxrc3q8pcGXf3HE/+QPNQRVAu6MfK0UcPYehPLTG59vuadEHFgI42naRJ6hHiRkmJ61pfVqyeFh80Uxa7pcfduGwvgxAziN2w96C+J4UhESY+j1jvkL+dB0h3oTOd0orWi1Ok/M6Bh8l+/Z61+9tQWHUnYcPi0ILARgCQ/LHq5h+7v6Ne8bYcnvRZ4ZvKEbaNr5u/WZ29dqfX7O+MuimcddNUsKC0PVZWI4gxK8rUsTplW5PEQt0/2tt/bluxcB+UKa/N1D4xoxqqmcBaOxDwY18J13oszb1iupvY+z5/fsL8rxNLE5y0XzI27CIGqtbvvlgPd+vxtK30n5QxK0M85zUcrD0xZa7XtkNNDh57j5SGwUWUKnQbFWho+dPUSnTNjned1NAZQ6a6kghvEqb7rsPMb2ntKT8e78/CxxCdV84rLZGWq9cE/qAeGar0RZ7ZPVL/u6qxEg9V6zAXpZ09t0R3Lgs19UGyaxsGRsUmNAdW+j66LaYx/7maNPa6RoN18NIUJAVc1dmja9LpQhj0lVSWXhtiPd4XbS+qKuTu1+sWj2nIgiGlUwz85owiszt12JPBlxt3TLWoENmrE+TO3FnzP73RUj6xtrrQ4qTE0OqaPXLsssKRqXoU180u11r8jGyJQ8QemqqZbTlSJwqI2kTw0YSdQkuorJWcjCXHTeUk86Hff/d/jmwq+d9Ez23XOjHXa2Bx/S3hfVnf8sI7PWnoQLaYzazhouW5f2jhpn9WSTN6A+pQNA46L17P5oTX7NW16XWJ6VnlV7dOPlpMvqKOvdGMriiOwEYBE1XUDKkvQY7tuXlw8+39SnXXLyljW+7Mnt8SyXlQm8CFcKMuBzn5fXbVLyVRP4uiQUk1HVJp+y5PrCweXm4/2S5J6Bgs86Eb4Q+9buS+6lRURxlS+SQrcSdKaFzsm/u21bPnuCUnZZ6gOlz63Q5LUPxTcLFqoHklrkAkbgQ3ktXR34UhqOadIS3dwgZIoz9EtPpN0xclLPataH7yTVgEOQ63dnCpx+uWL9P5fLw5ugZnji11QtrjP0Ti640a9yiAPz0LXm3X7juoLt6+a0jp81fO7Alpx4bfiPoayixbU5TitM16UIw2Xz7nbDmtfR3BBcT9yz7kkVGvKrXd0B9C7yQ+qR8ggsFEFsnNeBPXgGmaSPPgXRmtYUvx67i5Nm14Xaxm8dhm8at7u0h9C1ZkYihJi1bycS+6LAfZKCVvu75u9pUVHA0qI7GXbxbGtCpUrrKGNUdy2f/TYZq1s7NB+t9dKRnPW3+GdJ0l41AvWR69bVtb3/OxrguLefXvGOn3gqmiHHmdU01766VOb4y6CL//7yEb95/3Fcw36PY3KCcT6Xcf+jv6i+aBqEYGNAMR9SMV1EfZi/vYjWrq7Le5ipE7uMXX3C8EmxouLtVb3r9o36YHmxkUNMZboOC/3oFuXFB9SVc6YShQXdL6ZwZExXTl3pwZHvHfbzVRQklZ/mLf9cOkPuUbGChc+zIrRpMpdVq3tPx9Yr2/euzb49UV4DhashOYpQvZ2CCsZdbkPsGHNwhN3Dws4Ris8v5fvaddFz2wLqDTJVygJ9rfuq9fply+MuDTp1D3gvceGn6PTy327nOvOkxsOavbW4vdTv2dRpZe/UrMZ7T7So/deuUi3Lk3nUP+wENiAb34qT9+8r15fvXtNsOuPPZTk39ObDunOZY1lf7/gWO6Ee8sFc3XuU8fzhWw7dEznzdyqK+cG0225mhqion4GmL/9iA4HOEQsDI1tvfqfhzcGusyv3r1GNy3aqx897r1FaWIkSsIOuKCKMzOA4FGhymSxMvpNSnn1vF36QJ4hRn4qskEMSSlnEUGf3zNWNk1dR5m/7YN5Gkdy99vYuJ0y/OS7D6zT528LJw+VtdbXw1EUsrdJWEGb9p7gZzvJnsGnHF++a7V+80JTxeVI2vXTr+e3H9GBTn/XLD/11dxDKs2BwfGQOhn/46UL8r5ezqGV9MPxew+u176OPllr1dE7NanogU6nl9zaF0nGm43ARpUrN+twsRM+6RcDb6L9Ed9/aIMurtvh+fP9w/6TQCVxSqfeoVE94GZCl47/rj1HegJeU/7fvtzj8Z+ETXdsMNpM+d+8r16fvvmFyNZ374om3+sb8NGrwqs1biVgdWNHiU8ed3woSnBGPWawj+J621VgPHTgD5YVnmjXL2xQY4BDSnoGR/RCg/97ZBLugefP2jYl0BBmIODzt63U68+dPem157Yc1uqQKtV3LntRty0pvzEgbF6PgXyfK3YafCqEa3LSepolsa4ShW2HujVjlbfEsQnbZb6F1QAZxMxEUQniOD82MKrH1h3QaRfP11Y351/rsUGt8lF/qfbZZ3IR2AjAM5sOTfz79oR1CTqhzBMr7F4R+W72hVrvxsat7lzW6KvrOJIp6vrMl+9aPenvsFuMvJ43v8kaWrS3Lb48CYeK9NjoHx7V0Ghw59wFT2/T+hJdK3Ml4QFSkvqGnaBTkLmHvnlf/aS/E/JTJ/n+QxsqXkahoShhyc39kCv7GvC9BzfoS3euztsaVkyz21Lm53qWxP1bTG556/d1Siq9fYNY77p9nbrkuakNAdXyPFzsNMgeplnO/WpkbHxKTq6k9HJNRinic8b1y3X+zK1xFyMSSbl3BymKy0++zZYJvmeGMJ55w3KdffuqCEqTTgQ2ArD5wPGZM3713M4YSzL1YvL3r/2D4NcR+BKlJ9Yd0HsuW5i3FfXxdc26uG6HbnJzMVTjBTMIh7v9dZGMU/C7sPIlRnlYXfTM9ol/J3Hu+duX7tWbfj5XH7m2vMR2QdnXEd5DlNf9PX/7EQ2OjPv7kgeLd3nLPVRolYe6BkJrLc9YUuX5kTI9x4Z8JGeeueHglOMy954UVFLUpHhqw/GhSpl8DWHehzc15w+Axh3XyA40VBJkCSZAk38HvO+KRXrDebNlrfXcKyxqce/HNEj7NqKaXtjgyJjnYHq+oGRrj79AfK0hsBGAoKPh2w51694VTYEsK4wuf167u/oZbrB+v9MatDtPUrU+d27uHrerPhfM/O5ftb/0h2KW1FwFcfLcpTncYkxy82Kn55nfmSS8DKGas/WwTvvl8xO9QYZHx/Xg6v15E1hW2mNkRRnDDKYsY6/3Lp9R+tDVS0JJQhlWIslquXJvzHroLnTuZnq6tPvsCeJXmJfR3hJD48LqPVFssXEPYUjDEZzphfejxzfrdec6AQ6vQdRKHe4eVH0T4/3LlcTjK6xzLug6YFJ6JWXrHXKuod0DI7ppUYPGx62GRsf0xvPn6LSL58dcuupFYCOBzrh+uS542lsG6tyoXxSnttfARliZ3zFZU3ufpk2v0+FjyU4EKYXZlbiyBQdVrmqO1zy96VDJc//D1y4tuZxfPrtdHX3DanNbHW5a1KCfPbUlbwLLSrfn/B2tBd+L8hGpvXdIC3ceKeu7hSqAfvLwZCpYXsze0uL5s34l4fTIrqiXc3x5uVYc7UvPOPBCLvQ5C0b2tgzrOpikgHglRQlySFshj687IElasKPVd8LLcn3o6iU669YiyWSTs/s82bC/U9Om1xVNcjwwPKZfPrtd/cP5r7F+ZmlK0OFd0ujYuD554/LCsx6W+C1tIQd9k+SiZ7bpyrm7tHh3q1aWaCjJd7Sk6bhIAgIbAYjzoGsKqat21L8pO8FkUFY1doSQpDIeWw4eK/jewp2FH95wPFmkJH3rvnV6xyX5I+VBPOim9QbUkpNrI3dbNLT26PsPbdAPH91UcBk7Dxc+Rovp7He67feEkDy1WCtOlLvqfVcs0tfvqY8tT1CpB8JoZp+YeoYlZXpkX7OqxFDmwZEx9fkITmUc6hrQtOl1ZU25njkvC3l4TeF79hXurFeTg0hWqxs7phyLFz69TT99covSIKjre1j3iWnT66a8dqQnugYPrwHUNORKsdbq325eIUlaVuT8uXdlk+5a/qJuLZDottyeBFb+rzVR9lpo7x3WpgPd+tHj+esEJcuSgrrS8Oj4pOFcxYpc7N6eqdsMj5b+0bmfiGImpmpDYKPK5M6/Xe55UOz0C7XrfIB3/LNvX6V/uaZ0C3IaFKuYZlpm0iTKe9rnsqYjnL/jyERPgaTwWhkJsjLcmDXcYP3+Tl0xp/j0u5kcE4eKtFx94oboZlgJgpEz7GLa9DrtLhIADaIy0ef2rijWUhtma3SpJV+3YE/l6yhZfJuIwN9Zt6zQN+5ZW/b3s4+HsQI/KOjpud95yXy9+YK5vr+3wU3W+/Ba/w0HpfZVsftObj1Ekh6tb9bnb1+lZzZP7hF0z4omPZQVJAnrENl6sFtbsvKhzVjZpGV7yh+i4fW6ENbvScK55Fe+e11uotOk8FpPGHHLPxbW/KYpFfVMPGGcD284b7Y+caO3es1cD1MqE5iIBoGNEO0PMfHdcZPP5lsWVz4ry5oSCenCHjecsXR3m6ZNr5vamujhCrb90PHW46ASuR3qGtCVc3fmzQUQp7ASCb3Q0K7NB/zNYpFhrZ1I9jqZO21mgU3otUV7RUO7pk2vU0NA+QCCuimWc+MKs4K6dHfbxFzn2T5w1ZKJf3vp1ZSZXanYg/lwCInqKt00xbatMVKd+5CVPbNV0LKnEy3n0pGsq41/SavLdfQNa0EFvdyyf89AgeFA+ZKRVrIdCk0FHWYLrd8ll7r2ZXqXNnuYVSWMX3XmDcv18RuXT/x9/qxt+spda8peXtyBhTRfF4yMrLU62jesq5/fHXdxKpLZD0H35CpnaUnpASeVDtSHefx63Q5ehoRtbymvJ2q2sHt6pflaEAYCGyHq6As3APDWC+fqS3dOns6y2FhArz5328qiZ8poAJHpghWyrNpR5sE498Li5SR+fvvx8ey3BTQF72Wzd+qmRXu1scyH/Ww7Wo5N6rbZPzxadgbzsKLAX7pztedoda7dR3p15dypvQBKlfWff73Y0/Kf2ew8iDa6U6VWug2qNcfGV+9eo3+5enKvpS/eUXqasNyEYSe4d4ogfl+hCk++15Mwpj47V1A5pfn5rOPT+0Uxtj4fP6stt4iFzqHsxRWa7aKQ1Y0dk1rZg1ZOYCD7d77q917mY13xKWefJuHcy5XW5KEfzuk5GsS2vX7BHr3p53MqXk5c7lnRpL//5fNa3jC518zw6LiafCatLkepfZAZhlJ6Oc7/Zw7NhtZeffbWFRNDxxJ4GkUi6T97dGxcp1++KKK1OVvDqLxrGD09/CGwkWLHBkePT0NYSJknRLHW1xEP48SkMi/oeR9unP/PnNxelvubFS+WsfLiMt3wR8cqu2SPj1t99Lplk7pD/8MlC/S6c2dXtNwkydcV2YvcXA+o3EBOL5jcWT4mJf0rsAwvPTb8ytzg47pne/0plU55urfteCW9vGtiRatPlEM+p6T+/O2rJrWyhyVJLZ1ROxJQ0umkzh4UpHKne90VQq6vZXvaPSUQ3tmSnDxj2de/zEwtuVMn/+ypLXr/rxeruz/cvD+PlRjC67WRMBMc7XLLe9nsnVrb1DnRU+/2pflzb+RT6QNsJT24BkfGNG16ne5c5r28lQj6iuv3l49UWI8vh6egRk4lwU59acKm5vCC/mlGYAO+BXGT/sSNL5R8YMi9BmRa571cvItdPgaGx4rOluC1POXKlH5t1rRoPWUkhkuzoIcYJKVV5JH65riLEIjc3kOZQ99PYONYwHkGghbHIVOslbDQO4EMN4jx/IgiZNDRG8xwQy+yK6d+flsQ2+Hu5eUF7Ivdu/7hVwvKLM1kXXkeRMvpmbBsT1uiwkyHuwd1x9JGWWs9jaP3IsrRrDNW7YtuZR5lH4+5+zoTEOgrMMtIUFp9BPSch8v8O+2pDc5sXoW289M+hjl6aWQISybB5a1LJvdwLrd3URS9BINeRlgmJQCtYDm51/FMbqyk5qmJC4GNmO3v6NecrcHcLPMp1RI1Y2VTaOsupqG1Vz8ukE15Kueq4KfltFhkNDOMoVxJ6KKbvV/9XCijKnqhzR9UhTXo32FkApmxInsIlFfxH01T5Y7pz5xPfsr61gvn5Q1utOfkvDnqPhDlW3a443DjU27umiiUG8A92Dmg7z2wPtjCeFQq2F5oOEsCLuW+/OLZ7ZP+DrP8pZbtt0u117K2Rxik8uLbM+p1yXM7tK+jX2ubOidez+1RMDgypnX7iucnq0U/eXyznijSO6LQcdTY1qczb1hW1oxNc7Ye1mduWRFoXa3QzH3ZPU7OvGGZVjfm9oj0XobcT/q9Fpfb88xaq+8/tKGs7xbqnVvqVxd6v9x6mN9tFeUMMsfzsJRnk1tfKLcndK0hsBGASi6eH7pmib5z/7qJvx8qMoVaGM6f5W+u+igVukh72dy5F4CG1t6Ko5pBdVfOlKOSa1T2RTmIS92xwRFtPRhhtzZ3J5Z7oQ7jprTzcJtSc2wAACAASURBVHK67EbJy5Y8wT30/SbOPZanUpp7HmYSd247lCdJVxm7OXv55fSQKCaoerKf3DWBtGZFUIn7xbPbVbelpeD71sYXSCjVrdzfdK9TVWN1c3lW0ttyxZ0TIwiZluzRnGvfK37npZP+vvDpbfrMLSsjyQ+RJo/UN+uHjzmNWPnO/xMKHCLXL9yjrQePaeFO/40F331gndbt6wy0Z0yhWYDe+4aTJv699eCxid63mWO/qcQkAufP3Kq/+tlzed/r8Jn43u91/gcPb9ANC/ZocGRcKxvzDyUrdA5nrqkFA5FlXuzfeH5y88ZUGigzpowAjLUTwbMjx5I1o19SEdiIWXYl/MX2vknzuQc1m0faTRl24OE7L33J8atH67EhfejqJbromalBnDgqXvlmqYjbV+9aozNvCG4se8EeGzkt/1+9e3X+Dwa0vqgMj47rgqwkkWk2kie/ThjnSe4S8623nAfymW7X4FLaeoZCz8jfm5AhZlF3Cy647DK/99SGA6EObfL1mxP0rF7paek3mWu27Eq+l6C4n7LmuxZIwWz6Fp95Xg67QxbufqH4MKBMkvOuMnoY5DM6Nj7RUlstMvvV6Pi14IScAyOpvagKPdSeesorK1rujFX78jbwGEl/kBM8K6Tc+/PMjYd01fO71TNU+JjNV7ar5+0qOixuz5EebSqR9DnwHBs+j5ugj7Niy/MSEKnb3KK3Xzw/ltwf1YbARggy81/njlUrJbclszGAqSyfWF88QVKcSvWAyFyr91a4Hbr6nQBRZhrb7OktkzCspJR8PU16soYK+L1BjI/bKS3vG3MquFFN6ftCQzISzlXaoj17a4vuXVneWOa4n5M27p+87/NNVTmjzN8Wx+k1lrXS3NVHPRb1P7N645Wrkm34xTtW6YJZWyPpUVBo2+4+4ly/Z+cZcum1Pv7/Htmk6U9sLrtsQUpSotFKz68ght9JCjQoLkmXzt6Z9/Ug4qufu22lr89nEnQ+l9MbqZK6g5evXjt/j75+T33Z60iizDTL2cnpwx62mu22JXvLTo7pd297KX+pgKDX473Semz/UPZ1oPRKr1/YULR33gafAdMv3LFKL1ZxT6eJoSgFNu2crS363oPr1d47VFZgNO6GvaQhsBGCTvdBeu42/13oghTE1K9Ryx4OkDlZS3Xl86OhtVd3LDseaS4n0l3JLaStZ2jKLBWlXJinp8nAyJj+8/51mv7EZt8XtY9dv0x/WaDrY8Yja48nwTzzhmX+VpDHyoAz5kcZbfeiktlC8n2zrWdIH75mqZqPejv2B4bHpozt9cpLwtNSrZVhKW+aysLv+Q02T1m2z7N/2Z6p3fl3tOQZciOn3EOjTmb6oKzY21F2wM2vQr1TMq/P33HE88VzcGRMD+aMaQ+zG66voSgVViIrDdSH7eM3LNeyPaXzWfm9d7YmpBv1ke5gymElrd/fOeV1L1ul1HWkf3hU2w5FNzR0ZGxcz24+FFlDz+QgaDRPZS+29+nS2Tt1cd0O398tNoyuktIPjU6uC9oiQXkv/ARdB7Jm1An8wdhD4XM/8pTHnpb5XDVvV2CNuNOm12nNi0f1hdtXlfzswa4BXfrcDo2PW61+sXT9y7j/y7DWalVjh75zf+HcVAMeZj5KUrA9CQhsBCCoW0Gh7pd+ZA/B8DsePmilbt75LqZNHaWjtpXce1t78mfCXr6nXW/7xTz1DY1q0a4CM6YEcO14xyXz9cmbvI+vl6RVeYICRk4L6MNr/c/CUSyXRL6KzdaD+R/EismdEvcLdzg3icwmrLT+FPSRXfE0a5XkS8nz3Q/8erF2HenRb15oyv5kwWX8+InN+vztqyYNc8qd2SRM5V67snsKBXG5stZO6rGRK9/MDVH76HWFA4XlJMoL2uMh9fLLt1sK7apr5+/Rz57akv/NmJV9qXAvMkOlpmiPUL7gxJaD3Zr+RPDbPogHj4fWNGva9Dp1RNSjsJj7Vu7Tp29eoRVuLpLMsZw71KWcYMEVc3ZVXD4/blrUoP96cIOvxrgDnf1lN55lb5Goeod++c7Khr0Wqs8Wum+VMbNnxfwE3v/m58nNZeHXDQsbJv3tZdsXO3ZvX7o3b86R3OvlOffV67aljdp0oEsPrSlcF580K0rWIuq2tOjs3ABKzkExHGE9rloQ2AhAUBenIDLefv4dfxZASZKhcPJQf9vJS8vSlfN2qbN/RLuP9BQcOzjk9rSo+KE86/uX1G0v/MHM5/O8lvSkbI8V6AWQKXalQz9y90GlWyNpEW+v0/+OjI1r5d4O7XR7AWS6TXf3j5QVKMh3bHsJWnhp4c1ljCa1Sj6/fepQhcmBndIurtuh82cWznWyvSXZ877nBgSlYBJ/9g56z/WxL8AeclN4PM2CftgJ8nJZ6bLaEvBQnnG0L39ZktrbM5Nc/UCnv/I9sDq8XkuHuic3lhRrffUq6qmyD7u/IdPb2IvTL1+k91y2cOJvv/WypQVmuctc7ybqCgHVr3N7R/hVqBw3LmrI/4aXZeb8nVuv81ovqbQ+OGmWvQCulaXuWdZabc+XLDwiw6Pj+tdrlvr+Xu4xnkl4/mh9/qBtZlsudetHuT17m49OvY4FcbjXbW7xPeSumhDYSLByDvBX/e7LPH92VZld18OUucCOjdtAsrJnq/SCUSoZUjmyh8VELV8Xt6AqEYWizGEFEJKfKSUY+zv6Jz30/XreLn3hjlXa03q8e/uuwz069Rfz9Ng6/7158vHSehvEcTM4Mj7lmlRqGs9c96xomvR3brlWNVY2HWPYPbXDms5tb3twwx+stVq0s0CvtmLfk51yohaqRHsd2rX5QJduCvDBwq9yHigqSdgZtC1RzoQVIL+BjXOfSlZi59ycVtVgc576USXBhCDqCkVnxcrzVrGcSH4vzZX22PDz66PMFZc7zXHGRc9s0w8f3eRpGU9vOqT/uGdtkMXypVRjzfwd+e9vhbZyoVxFmcS4md3jpcdoObsy91j73oPrJ3IK1iICGwHIPajibPvNPidKnSBTukDF5K/Pmz3x70ykd3ORbOC3LS0v+VM1yb6RlVsBuHnx1AcCK+nS53boyrneusIe6OwPZAiVX1HOQe5FFPWKnsFRvffKRXr7xfMnXsvNXfKv1yzVbjcYUKhFrJTcStKCrOn2st+5dcleTZteF+iQl6CHiiTtOCkm1LIGuOi5246UXSn1/BtLfOzyOTvV0NqrT9z4Qt5rle9efVn//uRNL+jS5wqPw09a7664lLsVgngIO9iVnJnFSm2HfL92w/7SgY30XLkc+ZJOX/rc8SSwc/IkD87HSy6dbYe6JyWBD0q+BMcZUQQPKp5O1ONZWckw9ULBqt+80DQx3KzUz9gdwr7zYmB4TH993mzNy9M71BOfeVZyX79jWeOkHpFpqp+kyYlxF6AapGBijUTLviFmtmWhOcOTwO/FqNRNpFSrRr6b3aJd5T20Tl7v1IrIR69bOjGLQSld/cM6/fJF+tI/vFaX/Nvf5rxb/AZbbedMWD8nO2j6o8enzgqRr5Ws1Z2VqW+ovNaypnZvDw3Xzd8jqfgYUP/7OZwtWd90VG8+ubJp+YLgdSaooAVZgSqUp6hkGezxGcNKyddjI3v681sW79WsIsnmntncojP/9k91wgnl9ago1qsiex/dvLhBfcPTYu1WXYmwgzT5lp7Wa3+pchc6x36TJ/FyyQdYH9uod2hUL/+tZFbls5Nfb8iTaLVcZ1zvbRaez9y6UrO+957A1hu0oj1K5P9+4PU6vyynN3T2ekqtspxeamPjVi8pcS0O+krU2Tesg10Destrjt/3mzv7NTQ6risjymGTuzd2Hu4pmTuq2NCmgjMIJXxoetSSeTVMmaRG3ZJ+rBcrXpBTP/mJgoexJx9Ys7/o+x293se1Binf9vca1JCkYwPOuP2lPvIrBHZMBpxjw4uwhgmUY2RsXC99Sf4Od9c+v1uSyh7K9fEbvVUa/c7u40XQc7hbKx3qGtBZt67UJ049ufLlVfz9aI6hOVsP65Q//J2Jv8cD6FRz7lNbNDQ6rreeUl6AyFrvM1zl20q594RiSWK//9AGLdxxRNee/TZJUmPb1PvJ6Ni450BLtuypthfvatNij0HmqG/Hn7llhf75r0+SVGRGh4TXEdKg1Bm9cKf/Rggraa3HruRvuWCumi47I/TpZ/3I9yCbvQovh10lOTYyt+qghn2Vc932EjQMarP7fbB9scjMTKWSVXoaYpPz98bmTp325686/n4Et8FP3vSC9h/tV9NlZ4S/3oiuo4XKH+VQpDRgKEqM+oeLJ3Qr51zJPr4LJXCMyuwt/rt7BZUwKt/3A+syX6BsS3e3qflov7pyEnAdCjkRW9Iqp8Oj4yXnZ0/jdfjff7Om4HvLy0ieWYiX4+X1584u+ZmgeBkect2CPWUtO7fy56WLdjH5bvCZ6Ua3F5hmNSjW2pxpDINarv/vfOf+dTrzhuMBqtE8QbmewRE1+QggP7B6vx5fdyCUIQiNbb061+csKKUeHGZuPDTx78vn7Jzy/u3LsoY0+vhRuXlcvMr8+iCvfcWWtW5fp349b3dwK8tdd2hLTpcXS+SvKeeh46kNB9XnYZrHoFVSlcj+nZlcSbbA+57KMpFoPCiFAy2lRFVfKWc1n7ttpe/ZtFbkmWkvo9T9fnVZeaqiC/Jk7D8a3XC1cnu+RXFcPVrGzIlpR4+NEHh90NzbOrlSmTt1Z6XH/IIyErwFqW5LS9H3i0WZ80215EX/8KgOdg5M2geZ6U2bOvq1pUQC0HJv7C3dA/rq3ccffCOJEsesUCvGJXXbCyal63MfMq00JQFhfZP3G2alm/S7D6zTzV86zdd3lu0p3AMi+yGqUu/OyjRfjqgPt80HuvMOiXHKUiI7ehU9Hn3wqiVqbO9TwyUf1YkvOcH3OOIwrxP5gjqfvXWldh7u0RVnvdXXssIo5geuWiJJ+uY//aX+4tW/F8IapjrSXd6QmjQq2IU52mJICub4iSPPSaGHx1JlKTa9erUqlEzRj7D3cej1MuMk8vZVhqy/vf76qJNE/vTJqUNic02ZtS7nxxTqbdccUTAi6F0f1fW10HpeKNI798dPlN5f1YYeGyEo54I5OjY+MZVZ9nIum71z0pSIpSSt9d6vSm82331gvf7lmqVqzxrekT02+9LZU1vugnDvivzTyY2MjevWJXsrWrbX7ttelBswKia3ArK5SG+Ni55xprfd0XJM03NukOfMKJyRPFdu64+faeok6bkyehOFp/BBX87p3OtxqtigHPPZWpRkzUf79YZzZxdMTFe014Hb+yHTO2JFnspGyaH1ed4PohI2lmcsSuaB68d5creEwcvvaOl2eisd9DDrhZd7Xfa130t5IkkQWGRLtPUMadr0Oi3eFW+jhBfFtm3Umo/2a9r0Ok+zMgyPjeuJAHN4lVPnOuZj+uUodQ+MqCPA6YizN032qRV3OPua53frmvneezP1lXlP3deRv0fcDx7eoC/fuXrKtSDoaX5HxsYnNRgNjY5VHHQq59jNPUXW78ufbyVf3cVaW3A7Rq7AuV5uAv2gntcSNEo6EQhsJMQPH5t6Qx4cGdOtS/bqrFu8z0ecffOIMsgRVjdsv4p1sfPimU0tRVvmpfw35Y3N+S/UUUTTW0q0PGa3NJ1zX/3xNyaG/QRzVWxo7dWuwz1FH94qqQxba/XA6n0aGB6bsg9+4mFK0qISEhD8yl2rQ13+2hK9YkodCfvyBNkqSVxVqFVucGRMN5Q5vCWb1fFdW2wo2hJ3BpnntrRoeGxcjxV48PnFM9tL5v85oYLtUaqXW7nyDUUpV6Hp/oLwxTtWq/lov+oLVHz9+vtfPu9ryskgczvlyhwVxa6PP3hkgyTpxoXlT2FbSFvP0JR7dBxJuoO43QyNjqkha4rrb97r3NcyszKU8su67ZUXIkc19My8dPZOnZY165Yf+e4D2dN1e9k82XWRcnNEFZI9TbrfoZP9OcOCpk2vmwjCFmLkDCnKZ+bGQ87vy9ooy/e0T6p7BnE4XTZ7p866daW2HepWW8+QPvDrJXrj+XMCWHJxpXpi5rsdFbpr3r96v9535WJtbO7S3iK5QSKRVe7sSQEK9VAuVRXwe82ohmtMFAhsBKDcg+22pcdb8nO75WfLlyG+kBf2tk9EN6PsrnnN87v1hvNmT+QN8TJe+mDXgKZNrwu7aJ5uEJktdXeeDOZTlpdngavKGncYjezWhuzkjLctadS06XUFL8ql5G6HD129RB++dmnR72Rf6L1M65ZtwY5WnfvU1rzj5SvVmZDWx9ygWrHp58qRLzBRqWJjWYtduv7x0oVTeqNljo+bF+/VVc8Hkx/gUTfXULHAa+Y3ZAJva148qu8+sE4r9k7eH/O2H9G3Z9RP+X62zG8oJ+Bzb5n5G0oKsEJU7n7xehs7cszbEBGvW7dQQtp83Z5LFdHvWHa/XmhwAvNtAbaaZ7zjkvn674fWT3rtUAzDcbIfesptDPn1vN360NVLJvJZ7apg+kg/ga98rJVuWtQQ+rHhpRxJkZn5odXnPf7J9VMDAT0B92IIipfEpKVa8rN3Wf2+qXXIYreQ6xfs0ZfvLN4QkhkKc8OCBr3jkvk66Obvyg2+R93TO19j2uj4+JRyDI+Oa5nb6HC4e0AfvW5ZIOsK4ly5ISv4XHi618o3bG49YnmJhtdspYJv1YrARgD+f/buOz6O4vwf+LO6U+/VklUsyZIsy5Zsy7Lce7dswA1sMMZ00zEdTK+mpAKBkAQSQhoJ3wChQwgJISGEhF4ChPhHgEAgCb247e+P00p7py2zu7M7s3uf9+uVV7B0up3b2zL7zMzzpJ4jrBeJu54dHJ0zKkvnJnnSU298QLOvfKT/74K702n5QbSM8T/6k3UlENk42VNW2fiHvK+Hr4DXlFC7JrBUorj8vpdN85OkHu9Wx7/VqWE3c0SbppmanJUHrzN9/PIW58SzfvRffv3Su5a//9eH5gFMs9lRL7tM9Jk6EqSqRN951D5YuWPXHvroi530RP+Mlqf/+QHd89w7dOj3hwYx/HyAMJrtwXt7qUseg2J0XfByPLI+lO80eXg2Kpltt68nXeJuNJvI2cODk8EMJ+5/wfpc5a7/M79j8l157aOkjqRrfv/q+9R4xt30yrsf02v/Hhr00CdI/OEfjZeRsnr01ffoyvv/Rm8yLJ/yC+8lVO9/8iVddu9LpsmFjWb66NtgNGiR1EST5r5v0OfxWo3si527acqlv/b0HkYtuPMZ67xaiqI4unY7fQj+6oOv2M5q0QYOHvu7eXnXIFydMgPNbLf8I6V61ewrfzPwWkVRXAVCn+4PQO3avWegkhuPZ6NHXmFYLmizn//icGaiohBtcDCr12lgMSoQ2JCE0fE/cKHjeM868Ht/omsefpVLcic/yDTqINruParpWv+gXffI32nva5PLgD7aXwkkdRaA2Xf421feox0eynlq/RujIGCYvS+o3G8QPt2xi+6wSKyaOttDG+FymifklXc/poNuHFq1hjUI9tmO3dR1/gOOtumGDJe3r3KaCeOUqGv7LY97e3DV/PfTHUKWW/71DfPO707GOr6i76urr/tDoNu7+7nENefP2/9Lq22W8notMf3FTvFLcNvPuY+az7qH2/v1XPwQffu3r9OKq4eW/l72jUfpFIOl06m+87vXk0qH6h8mr/+dt7xjTrSfcx+9wzgLzIxR4EghxXJ5I0uwyarSGg//6w/g2S2PPPP/PC7ltfGwbkb6Vff/zbT62espgbR/ffiF52uXds3efMtfaJ9rH/P2ZibcLsd9mKHAA0q5OofAhiSMDt3BGRvuDuzUCPD6Gx6nR199n6564BXu6+wGoqpc35UP3p1R3p/R6iHuSAcJNd1yOzr43d8bj4Q/bTJF86AbnzAckWGlLalRyNlIiBkvbdF7XfS6TwdSR2781vfN39M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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1d8c8358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "delta = 10\n",
    "def increments(delta):\n",
    "    increments = []\n",
    "    i=0\n",
    "    while i+delta<len(prices):\n",
    "        diff = prices[i+delta]-prices[i]\n",
    "        increments.append(diff)\n",
    "        i += 1\n",
    "    return increments\n",
    "\n",
    "incr = increments(10)\n",
    "fig = plt.gcf()\n",
    "fig.set_size_inches(18.5, 10.5) \n",
    "plt.plot(range(len(incr)),incr)\n",
    "plt.title(\"Retours du Modèle de Maslov pour N=%i et qlo=%.1f\" %(N,qlo))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-2.48982888 -2.48982888  9.43534465 ...  9.43534465 -2.48982888\n",
      " -2.48982888]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c23d6bd68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import scipy\n",
    "from scipy import signal\n",
    "from numpy import fft\n",
    "def correlation(x):\n",
    "    return scipy.signal.correlate(x,x)\n",
    "\n",
    "correlation = correlation(x)\n",
    "print(correlation)\n",
    "\n",
    "Fs = 150\n",
    "n = len(correlation) # length of the signal\n",
    "k = np.arange(n)\n",
    "T = n/Fs\n",
    "frq = k/T # two sides frequency range\n",
    "frq = frq[range(math.floor(n/2))] # one side frequency range\n",
    "\n",
    "\n",
    "log = lambda x: math.log(x) if x > 0 else 0\n",
    "\n",
    "Y = np.fft.fft(correlation)/n\n",
    "Y = Y[range(math.floor(n/2))]\n",
    "plt.plot(list(map(log, frq)), list(map(log, abs(Y))),'r')\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112c23860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def log_increments(delta):\n",
    "    increments = []\n",
    "    i=0\n",
    "    while i+delta<len(prices):\n",
    "        diff = math.log(prices[i+delta])-math.log(prices[i])\n",
    "        increments.append(diff)\n",
    "        i += 1\n",
    "    return increments\n",
    "\n",
    "fig = plt.gcf()\n",
    "fig.set_size_inches(18.5, 10.5)\n",
    "ax = plt.gca()\n",
    "ax.set_xlim(-0.01,0.01)\n",
    "\n",
    "#sns.distplot(incr, bins=500, hist=True)\n",
    "plt.hist(log_increments(1), bins=500, color='r')\n",
    "#plt.hist(log_increments(10), bins=500, color='b')\n",
    "#plt.hist(log_increments(100), bins=500, color='g')\n",
    "plt.show()\n",
    "#plt.title(\"Distribution des retours du Modèle de Maslov pour N=%i et qlo=%.1f\" %(N,qlo))\n",
    "#plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda3/lib/python3.6/site-packages/matplotlib/ticker.py:2206: UserWarning: Data has no positive values, and therefore cannot be log-scaled.\n",
      "  \"Data has no positive values, and therefore cannot be \"\n",
      "/anaconda3/lib/python3.6/site-packages/matplotlib/axes/_base.py:3291: UserWarning: Attempted to set non-positive ylimits for log-scale axis; invalid limits will be ignored.\n",
      "  'Attempted to set non-positive ylimits for log-scale axis; '\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a23581e10>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a236a2da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "incr = log_increments(10)\n",
    "\n",
    "f, ax = plt.subplots(figsize=(18.5, 10.5))\n",
    "ax.set(xscale=\"log\", yscale=\"log\")\n",
    "sns.distplot(incr, ax=ax, hist=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11cd4e7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.sort(np.array(incr))\n",
    "y = np.arange(1, len(x)+1)/len(x)\n",
    "plt.plot(x,y,'.', linestyle='none')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'powerlaw_gen' object has no attribute 'Fit'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-9-fb7bdeaacd88>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      7\u001b[0m     \u001b[0;32melif\u001b[0m \u001b[0ml\u001b[0m\u001b[0;34m<\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      8\u001b[0m         \u001b[0mincrN\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0ml\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 9\u001b[0;31m \u001b[0mresults\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpowerlaw\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mFit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mincrP\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     10\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mresults\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpower_law\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0malpha\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     11\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mresults\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpower_law\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mxmin\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mAttributeError\u001b[0m: 'powerlaw_gen' object has no attribute 'Fit'"
     ]
    }
   ],
   "source": [
    "from scipy.stats import powerlaw\n",
    "incrP = []\n",
    "incrN = []\n",
    "for l in incr:\n",
    "    if l>0:\n",
    "        incrP.append(l)\n",
    "    elif l<0:\n",
    "        incrN.append(-l)\n",
    "results = powerlaw.Fit(incrP)\n",
    "print(results.power_law.alpha)\n",
    "print(results.power_law.xmin)\n",
    "#R, p = results.distribution_compare('power_law', 'lognormal')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "results = powerlaw.Fit(incrN)\n",
    "print(results.power_law.alpha)\n",
    "print(results.power_law.xmin)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda3/lib/python3.6/site-packages/matplotlib/ticker.py:2206: UserWarning: Data has no positive values, and therefore cannot be log-scaled.\n",
      "  \"Data has no positive values, and therefore cannot be \"\n",
      "/anaconda3/lib/python3.6/site-packages/matplotlib/axes/_base.py:3291: UserWarning: Attempted to set non-positive ylimits for log-scale axis; invalid limits will be ignored.\n",
      "  'Attempted to set non-positive ylimits for log-scale axis; '\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a1fce8da0>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112c7e780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, ax = plt.subplots(figsize=(18.5, 10.5))\n",
    "ax.set(xscale=\"log\", yscale=\"log\")\n",
    "sns.distplot(incrN, ax=ax, hist=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[6.90707119 6.90808319 6.90800893 ... 6.46357413 6.46445173 6.46697491]\n",
      "Hurst(GBM):   0.49333430427527686\n",
      "Hurst(MR):    -0.00023716751006540461\n",
      "Hurst(TR):    0.954539284690898\n",
      "Hurst(Maslov):  0.25800854947601415\n"
     ]
    }
   ],
   "source": [
    "from numpy import cumsum, log, polyfit, sqrt, std, subtract\n",
    "from numpy.random import randn\n",
    "def hurst(ts):\n",
    "    \"\"\"Returns the Hurst Exponent of the time series vector ts\"\"\"\n",
    "    # Create the range of lag values\n",
    "    lags = range(2, 100)\n",
    "\n",
    "    # Calculate the array of the variances of the lagged differences\n",
    "    tau = [sqrt(std(subtract(ts[lag:], ts[:-lag]))) for lag in lags]\n",
    "\n",
    "    # Use a linear fit to estimate the Hurst Exponent\n",
    "    poly = polyfit(log(lags), log(tau), 1)\n",
    "\n",
    "    # Return the Hurst exponent from the polyfit output\n",
    "    return poly[0]*2.0\n",
    "\n",
    "# Create a Gometric Brownian Motion, Mean-Reverting and Trending Series\n",
    "gbm = log(cumsum(randn(100000))+1000)\n",
    "print(gbm)\n",
    "mr = log(randn(100000)+1000)\n",
    "tr = log(cumsum(randn(100000)+1)+1000)\n",
    "\n",
    "# Output the Hurst Exponent for each of the above series\n",
    "# and the price of Google (the Adjusted Close price) for \n",
    "# the ADF test given above in the article\n",
    "print(\"Hurst(GBM):   %s\" %(hurst(gbm)))\n",
    "print(\"Hurst(MR):    %s\" %(hurst(mr)))\n",
    "print(\"Hurst(TR):    %s\" %(hurst(tr)))\n",
    "\n",
    "#prices = Maslov_model(N,buy_sell_param,qlo,bid_limit_orders, ask_limit_orders, initialPrice,)\n",
    "# Assuming you have run the above code to obtain 'goog'!\n",
    "print(\"Hurst(Maslov):  %s\" %(hurst(prices)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(\"===  Loading Data ===\")\n",
    "\n",
    "apple_address = \"apple.csv\"\n",
    "apple_pd = pd.read_csv(apple_address, header=0)\n",
    "apple_matrix = apple_pd.as_matrix()\n",
    "print(\"Hurst(Apple):  %s\" %(hurst(apple_pd['Adj Close'])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#results = powerlaw.Fit(y)\n",
    "#print(results.power_law.alpha)\n",
    "#print(results.power_law.xmin)\n",
    "powerlaw.plot_ccdf(incrN, color='b')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from pandas import Series, DataFrame, Panel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def product_sign(t):\n",
    "    signs = []\n",
    "    for t_prim in range(N):\n",
    "        if t_prim + t + 1 < N:\n",
    "            sign = (np.sign(prices[t_prim + t + 1] - prices[t_prim + t]) * np.sign(prices[t_prim + 1] - prices[t_prim]))\n",
    "            signs.append(sign)\n",
    "    return signs\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "autocorrelation_sign_functions = []\n",
    "\n",
    "for t in range(N):\n",
    "    sign_temp_mean = np.mean(product_sign(t))\n",
    "    autocorrelation_sign_functions.append(sign_temp_mean)\n",
    "\n",
    "x = np.linspace(0, 1 * 0.5, N * 0.5)\n",
    "plt.plot(x, scipy.fftpack.fft(autocorrelation_sign_functions))\n",
    "plt.title(\"Autocorrelation function of the absolute value of price increments\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "autocorrelation_abs_value_functions = []\n",
    "\n",
    "def product_abs(t):\n",
    "    products = []\n",
    "    for t_prim in range(N):\n",
    "        if t_prim + t + 1:\n",
    "            term1 = math.fabs(np.sign(prices[t_prim + t + 1] - prices[t_prim + t]))\n",
    "            term2 = math.fabs(np.sign(prices[t_prim + 1] - prices[t_prim]))\n",
    "            products.append(term1 * term2)\n",
    "    return products\n",
    "\n",
    "for t in range(N):\n",
    "    abs_value_mean = np.mean(product_abs(t))\n",
    "    autocorrelation_abs_value_functions.append(abs_value_mean)\n",
    "\n",
    "x = np.linspace(0, 1 * 0.5, N * 0.5)\n",
    "plt.plot(x, scipy.fftpack.fft(autocorrelation_abs_value_functions))\n",
    "plt.title(\"Autocorrelation function of signs of price increments\")\n",
    "plt.show()\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mean(series):\n",
    "    m = 0\n",
    "    for p in series:\n",
    "        m += p\n",
    "    m = m / len(series)\n",
    "    return m\n",
    "\n",
    "def hurst_exponent(series):\n",
    "    m = mean(series)\n",
    "    \n",
    "    adjusted_series = [0] * len(series)\n",
    "    progressive_means = [0] * len(series)\n",
    "    cumulative_deviate_series = [0] * len(series)\n",
    "    range_series = [0] * len(series)\n",
    "    standard_deviation_series = [0] * len(series)\n",
    "    rescaled_range_series = [0] *len(series)\n",
    "    for t in range(len(series)):\n",
    "        adjusted_series[t] = series[t] - m\n",
    "        temp = 0\n",
    "        progressive_means[t] = mean(series[:t+1])\n",
    "        for t_prim in range(t + 1):\n",
    "            cumulative_deviate_series[t] += adjusted_series[t_prim]\n",
    "            temp += (series[t_prim] - progressive_means[t]) ** 2\n",
    "        range_series[t] = max(cumulative_deviate_series[:t + 1]) - min(cumulative_deviate_series[:t + 1])\n",
    "        standard_deviation_series[t] = math.sqrt(temp / (t + 1))\n",
    "        if standard_deviation_series[t] != 0:\n",
    "            rescaled_range_series[t] = range_series[t] / standard_deviation_series[t]\n",
    "    \n",
    "    return rescaled_range_series\n",
    "\n",
    "     "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = range(1, N + 1)\n",
    "y = hurst_exponent(prices)\n",
    "plt.plot(x, math.log(10, y))\n",
    "plt.title(\"Hurst exponent of price series\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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